Mr Raab described the president as "effusive in his warmth" for the United Kingdom, adding: 'It was awesome to hear an American president talk about our country in such warm terms'.
The Daily Telegraph reported that Cummings had threatened Downing Street staff with the sack if they tried to block no-deal and accused former ministers including Philip Hammond of seeking to frustrate Brexit.
No further details of the meeting with Mr Trump were immediately available.
Mr Raab said today: 'We appreciate the President's warmth and enthusiasm for the UK-US relationship.
He flew into the USA capital following talks on Tuesday in Toronto with Canadian foreign minister Chrystia Freeland and is due to travel on to Mexico following his meetings in Washington.
He said that a "new state" with a new constitution would be required for a united Ireland.
Meanwhile Britain's International Trade Secretary Liz Truss, traveling with Raab, had lined up meetings with top American officials including Trade Representative Robert Lighthizer and Commerce Secretary Wilbur Ross.
The Brexit negotiations have descended into a game of chicken, with the European Union repeating that it is unwilling to reopen talks on the binding part of the deal Theresa May struck.
"We will see it as giving Britain an artificial comparative advantage and make us think about the need to retaliate against Britain, not to welcome Britain with new trade agreements", he said.
The Irish economy is considered the most vulnerable among remaining European Union members to Brexit and Ireland faces a 12-fold rise in the number of import and export declarations made by local companies in the event of a no-deal British exit. European Commission spokeswoman Annika Breidthardt told reporters in Brussels on Tuesday that, while the EU is open to talks, the bloc's own stance "remains unchanged".
"What I am saying is it doesn't end of the 31st of October, if we have no deal we are going to have to talk and the first things on the agenda are going to be citizens' rights, the financial settlement and the solution to the Irish border, before we even start to talk about a free trade agreement".